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SpeedInfTradeoff SIGNED

Speed-Information Tradeoffs: Beyond Quasi-Entropy Analysis

Total Cost €


EC-Contrib. €






Project "SpeedInfTradeoff" data sheet

The following table provides information about the project.


Organization address
city: HAIFA
postcode: 32000

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Total cost 1˙515˙801 €
 EC max contribution 1˙515˙801 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-CoG
 Funding Scheme ERC-COG
 Starting year 2016
 Duration (year-month-day) from 2016-06-01   to  2021-05-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

The starting point of this research proposal is a recent result by the PI, making progress in a half century old, notoriously open problem. In the mid 1960’s, Tukey and Cooley discovered the Fast Fourier Transform, an algorithm for performing one of the most important linear transformations in science and engineering, the (discrete) Fourier transform, in time complexity O(n log n). In spite of its importance, a super-linear lower bound has been elusive for many years, with only very limited results. Very recently the PI managed to show that, roughly speaking, a faster Fourier transform must result in information loss, in the form of numerical accuracy. The result can be seen as a type of computational uncertainty principle, whereby faster computation increases uncertainty in data. The mathematical argument is established by defining a type of matrix quasi-entropy, generalizing Shannon’s measure of information (entropy) to “quasi-probabilities” (which can be negative, more than 1, or even complex). This result, which is not believed to be tight, does not close the book on Fourier complexity. More importantly, the vision proposed by the PI here reaches far beyond Fourier computation. The computation-information tradeoff underlying the result suggests a novel view of complexity theory as a whole. We can now revisit some classic complexity theoretical problems with a fresh view. Examples of these problems include better understanding of the complexity of polynomial multiplication, integer multiplication, auto-correlation and cross-correlation computation, dimensionality reduction via the Fast Johnson-Linednstrauss Transform (FJLT; also discovered and developed by the PI), large scale linear algebra (linear regression, Principal Component Analysis - PCA, compressed sensing, matrix multiplication) as well as binary functions such as integer multiplication.


year authors and title journal last update
List of publications.
2018 Ivo F. D. Oliveira, Nir Ailon, Ori Davidov
A New and Flexible Approach to the Analysis of Paired Comparison Data
published pages: 1=20, ISSN: 1533-7928, DOI:
JMLR Volume 19, Number 60 2019-08-05
2020 Nir Ailon
Paraunitary Matrices, Entropy, Algebraic Condition Number and Fourier Computation
published pages: , ISSN: 0304-3975, DOI:
Theoretical Computer Science 2019-08-05
2018 Elad Hoffer, Itay Hubara, Daniel Soudry
Fix your classifier: the marginal value of training the last weight layer
published pages: , ISSN: , DOI:
International Conference on Learning Representations (ICLR) 2019 This is an annual conference. 2019-05-22

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